Method for finishing surface of preliminary polished glass substrate

ABSTRACT

A glass substrate obtained by a method including measuring flatness of a glass substrate surface and measuring concentration distribution of dopant in the substrate. Processing conditions of the surface are set up for each site of the substrate based on results from the measuring the flatness and the measuring the distribution, and the finishing is carried out while keeping an angle formed by normal line of the substrate and incident beam onto the surface at from 30 to 89°. The surface is subjected to second finishing for improving an RMS in a high spatial frequency region. The surface after the second finishing satisfies the requirements: an RMS slope in the region that 5 μm&lt;λ (spatial wavelength)&lt;1 mm is not more than 0.5 mRad and an RMS slope in the region that 250 nm&lt;λ (spatial wavelength)&lt;5 μm is not more than 0.6 mRad.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims benefit of priorityfrom U.S. application Ser. No. 12/815,091, filed Jun. 14, 2010, which isa divisional of and claims benefit of priority from U.S. applicationSer. No. 12/475,878, filed Jun. 1, 2009, the entire contents of each ofwhich are hereby incorporated by reference. U.S. application Ser. No.12/475,878 is a continuation of PCT/JP2007/72689, filed Nov. 22, 2007,and is based on Japanese Patent Application No. 2006-325286, filed Dec.1, 2006.

TECHNICAL FIELD

The present invention relates to a method for finishing a pre-polishedglass substrate surface. In particular, the invention relates to amethod for finishing a surface of a glass substrate required to havehigh flatness, like glass substrates for use as reflective type masksfor EUV (extreme ultraviolet) lithography in semiconductor productionsteps. Furthermore, the invention relates to a glass substrate finishedusing the method of the invention. Furthermore, the invention relates toa photomask and a mask blank using the glass substrate and to anexposure tool using the glass substrate as an optical element of anoptical system.

BACKGROUND ART

In the lithographic technology, lithographic exposure tools fortransferring a fine circuit pattern onto a wafer to produce anintegrated circuit have hitherto been extensively used. With the trendtoward a high degree of integration, a high speed and a high function inan integrated circuit, the integrated circuits are becoming finer, andthe exposure tools are required to have a large focal depth and form ahigh-resolution circuit pattern image on a wafer surface. Thewavelengths of exposure light sources are becoming shorter. ArF excimerlasers (wavelength: 193 nm) have come to be used as exposure lightsources in place of the g-line (wavelength: 436 nm), i-line (wavelength:365 nm) and KrF excimer lasers (wavelength: 248 nm) heretofore in use.Furthermore, use of an F₂ laser (wavelength: 157 nm) as an exposurelight source for conforming to next-generation integrated circuitshaving a line width of not more than 100 nm is thought to be promising.However, the generations which can be covered by this light source areregarded as being limited to ones with line widths down to 70 nm.

Under such technological trends, a lithographic technique employing EUVlight as a next-generation exposure light source is thought to beapplicable to plural generations of 45 nm and finer and is attractingattention. The EUV light as referred to herein refers to light having awavelength band in the soft X-ray region or vacuum ultraviolet region.Specifically, it refers to light having a wavelength of from about 0.2to 100 nm. At present, use of a lithographic light source of 13.5 nm isbeing investigated. The exposure principal in this EUV lithography(hereinafter abbreviated as “EUVL”) is equal to that in the conventionallithography in the point that a mask pattern is transferred with anoptical projection system. However, since there is no material whichtransmits light in the EUV light energy region, a refractive opticalsystem cannot be used, and a reflective optical system should be used(see Patent Document 1).

The reflective type mask for use in EUVL is basically constituted of (1)a glass substrate, (2) a reflecting multilayered film formed on theglass substrate and (3) an absorber layer formed on the reflectingmultilayered film. As the reflecting multilayered film, a film having astructure formed by periodically stacking, in an nm-order thickness,materials having a different refractive index at the wavelength of theexposure light from each other is used. Known typical materials are Moand Si.

Furthermore, Ta and Cr are being investigated for the absorber layer.The glass substrate is required to be made of a material having a lowcoefficient of thermal expansion so as not to be distorted even uponirradiation with EUV light. Use of a glass having a low coefficient ofthermal expansion or a crystallized glass having a low coefficient ofthermal expansion is being investigated. In this description, a glasshaving a low coefficient of thermal expansion and a crystallized glasshaving a low coefficient of thermal expansion are hereinafter referredto inclusively as “low-expansion glass” or “ultralow-expansion glass”.

The low-expansion glass or ultralow-expansion glass most widely used inEUVL reflective type masks is quartz glass which comprises SiO₂ as amain component and to which TiO₂, SnO₂ or ZrO₂ is added as a dopant forthe purpose of reducing a coefficient of thermal expansion of glass.

A glass substrate is produced by processing such a glass or crystallizedglass material with high accuracy and cleaning it. In the case ofprocessing a glass substrate, in general, a surface of the glasssubstrate is pre-polished at a relatively high processing rate until theglass substrate surface has given flatness and RMS in a high spatialfrequency (HSFR) region; and thereafter, the glass substrate surface isfinished by a method having higher processing accuracy or underprocessing conditions bringing about higher processing accuracy so as toresult in desired flatness and RMS in an HSFR region.

Patent Document 2 discloses that the polishing method and devicedisclosed therein are suitable for polishing processing of an opticalelement with high accuracy comprising a fluoride based crystal materialsuch as calcium fluoride, magnesium fluoride, etc., which is suitablefor various optical elements used over a wide wavelength range of from avacuum ultraviolet region to a far-infrared region, lenses, windowmaterials, prisms, etc. Furthermore, Patent Document 3 discloses thatthe production method of a glass substrate for use in mask blanksdisclosed therein reduces or eliminates adverse influences by striae ofthe glass substrate for use in mask blanks or by reflection on the backsurface, measures the irregular shape on the surface of the glasssubstrate to be measured with high accuracy, and controls the flatnesswith extremely high accuracy based on the measurement results, therebyrealizing a high flatness.

The polishing method and device described in Patent Document 2 are basedon the assumption that in the case of works comprising a crystalmaterial are uniformly polished at a constant rate and a constantpressure utilizing a tool which is sufficiently small relative to theworks, the removal amount is equal. However, the polishing tooldisclosed in this patent document is one prepared by laminating acircular pitch or foamed polyurethane, as a polishing pad, onto a basemetal; in the polishing method described in this patent document, such apolishing tool is pressed against the surface to be processed whilebeing rotated and while applying a polishing liquid containing diamondfine powder thereto and continuously moved and scanned from end to endon the lens surface. Therefore, there is a concern that even whenpolishing is uniformly effected at a constant rate and a constantpressure, the polishing amount does not become constant depending uponthe abrasion and clogging of the polishing pad and the concentration andentrance of the diamond slurry to the polishing pad.

In the method disclosed in Patent Document 3, it is necessary to makethe distance L1 between surfaces A and B and the distance L2 betweensurfaces C and D relatively large in the surface shape measurementdevice 2 shown in FIG. 2 of this patent document. Specifically, it isnecessary that the distances L1 and L2 are made to be about several tensmm. In measuring the surface shape, it is liable to be influenced by airfluctuation of this space. In particular, when a downflow is applied forthe purpose of increasing the degree of cleanness within the surfaceshape measurement processing device, the influences of air fluctuationbecome remarkable.

Patent Document 1: JP-T-2003-505891

Patent Document 2: JP-A-2003-159636

Patent Document 3: JP-A-2006-133629

DISCLOSURE OF THE INVENTION

Problems that the Invention is to Solve

There may be the case where, when a glass substrate for use in an EUVLreflective type mask is processed, partial waviness is generated on theglass substrate surface. The present inventors have found that thegeneration of this waviness is attributable to a partial difference inthe composition of the glass substrate, more specifically, to thedistribution of the concentration of the dopant contained in the glasssubstrate. There is a concern that waviness may be caused on the glasssubstrate surface upon each of pre-polishing and finishing. However,there is a concern that pre-polishing with a high processing rate maycause larger waviness on the glass substrate surface. In the case wherepre-polishing caused large waviness, it was difficult for finishing toremove the waviness, thereby making the glass substrate surface have adesired flatness. Furthermore, there may also be the case where thewaviness caused during the pre-polishing grows to larger waviness duringthe finishing.

In order to solve the foregoing problems, an object of the invention isto provide a method in which waviness generated on a glass substratesurface during pre-polishing is removed, and the glass substrate isfinished so as to have a surface which is excellent in flatness.

Furthermore, an object of the invention is to provide a method in whichthe glass substrate processed so as to have a surface which is excellentin flatness is further finished into a surface which is excellent in anRMS slope and an RMS in an HSFR region.

Furthermore, an object of the invention is to provide a glass substratefinished by the foregoing method of the invention, which is excellent inan RMS slope, an RMS in an HSFR region and flatness.

Furthermore, an object of the invention is to provide a photomask and amask blank using the foregoing glass substrate.

Furthermore, an object of the invention is to provide an exposure toolwhich is used as an optical element of an optical system using theforegoing glass substrate.

Means for Solving the Problems

In order to achieve the foregoing objects, the invention provides amethod for finishing a pre-polished glass substrate surface using anyone of processing methods selected from the group consisting of ion beametching, gas cluster ion beam etching and plasma etching, the glasssubstrate being made of quartz glass that contains a dopant andcomprising SiO₂ as a main component, and the method for finishing apre-polished glass substrate surface comprising the steps of:

measuring flatness of the glass substrate surface using a shapemeasurement unit that comprises: a low-coherent light source whoseoutgoing light flux has a coherence length shorter than twice an opticaldistance between front and back surfaces of the glass substrate; a pathmatch route part that divides the outgoing light flux from thelow-coherent light source into two light fluxes, causes one of the twolight fluxes to make a detour by a given optical path length relative tothe other light flux, and then recombines the light fluxes into a singlelight flux and outputs it; and an interference optical system thatacquires an interference fringe which carries wave surface informationof the glass substrate surface by radiating an outgoing light flux fromthe low-coherent light source onto a reference surface and the glasssubstrate surface held on a measurement optical axis and making lightsreturning from the reference surface and the glass substrate surfaceinterfere with each other, and

measuring a concentration distribution of the dopant contained in theglass substrate,

wherein processing conditions of the glass substrate surface are set upfor each site of the glass substrate based on results obtained from thestep of measuring a surface shape of the glass substrate and the step ofmeasuring a concentration distribution of the dopant contained in theglass substrate, and the finishing is carried out while keeping an angleformed by a normal line of the glass substrate and an incident beam ontothe glass substrate surface at from 30 to 89° (this method will behereinafter referred to as “finishing method the invention”).

In the finishing method of the invention, it is preferred thatcorrelation between the concentration of the dopant contained in theglass substrate and the processing rate of the glass substrate surfaceis determined beforehand,

that after measuring the flatness of the glass substrate surface, agiven amount of the glass substrate surface is processed under certainprocessing conditions, and the flatness of the glass substrate surfaceafter the processing is then measured, and

that the concentration distribution of the dopant contained in the glasssubstrate is measured using a difference in the flatness of the glasssubstrate surface before and after the processing and the correlationbetween the concentration of the dopant and the processing rate.

In the finishing method of the invention, it is preferred that theflatness of the glass substrate surface before and after the processingis measured using the shape measurement unit comprising the low-coherentlight source, the path match route part and the interference opticalsystem.

In the finishing method of the invention, it is preferred that the widthof waviness present on the glass substrate surface is specified from theresults of the step of measuring flatness of the glass substratesurface, and

that the processing is carried out using a beam having a beam diameterof not more than the width of the waviness in terms of an FWHM (fullwidth of half maximum) value.

It is more preferred that the FWHM value of the beam diameter is notmore than one-half the width of the waviness.

In the finishing method of the invention, it is preferred that theprocessing method is gas cluster ion beam etching; and it is preferredto use, as a source gas of the gas cluster ion beam etching, any one ofmixed gases selected from the group consisting of a mixed gas of SF₆ andO₂, a mixed gas of SF₆, Ar and O₂, a mixed gas of NF₃ and O₂, a mixedgas of NF₃, Ar and O₂, a mixed gas of NF₃ and N₂ and a mixed gas of NF₃,Ar and N₂.

In the finishing method of the invention, it is preferred that the glasssubstrate is made of a low-expansion glass having a coefficient ofthermal expansion at 20° C. of 0±30 ppb/° C.

In the finishing method of the invention, it is preferred that thedopant is TiO₂. In the finishing method of the invention, it ispreferred that the glass substrate has an RMS in a high spatialfrequency (HSFR) region of the substrate surface after the pre-polishingof not more than 5 nm.

In the finishing method of the invention, it is preferred that the glasssubstrate surface finished by setting up the processing conditions foreach site of the glass substrate is further subjected to secondfinishing for improving an RMS in a high spatial frequency (HSFR)region.

It is preferred that the second finishing is carried out by gas clusterion beam etching while keeping an angle formed by a normal line of theglass substrate and an incident gas cluster ion beam into the glasssubstrate surface at from 30 to 89° and using, as a source gas, an O₂single gas or a mixed gas of O₂ and at least one gas selected from thegroup consisting of Ar, CO and CO₂ at an accelerating voltage of 3 kV ormore and less than 30 kV.

Furthermore, it is preferred that the second finishing is carried out bymechanical polishing using a polishing slurry at a surface pressure offrom 1 to 60 g_(f)/cm².

Furthermore, the invention provides a glass substrate having a substratesurface that satisfies the following requirements (1) and (2) (thisglass substrate will be hereinafter referred to as “glass substrate (1)of the invention”).

(1) an RMS slope in the region that 5 μm<λ (spatial wavelength)<1 mm isnot more than 0.5 mRad.

(2) an RMS slope in the region that 250 nm<λ (spatial wavelength)<5 μmis not more than 0.6 mRad.

Furthermore, the invention provides a glass substrate having a substratesurface that satisfies the following requirements (3) and (4) (thisglass substrate will be hereinafter referred to as “glass substrate (2)of the invention”).

(3) an RMS slope in the region that 2.5 μm<λ (spatial wavelength)<1 mmis not more than 0.45 mRad.

(4) an RMS slope in the region that 250 nm<λ (spatial wavelength)<2.5 μmis not more than 0.5 mRad.

Furthermore, the invention provides a glass substrate having a substratesurface that satisfies the following requirements (5) and (6) (thisglass substrate will be hereinafter referred to as “glass substrate (3)of the invention”).

(5) an RMS in the region that 100 nm<λ (spatial wavelength)<1 μm is notmore than 0.1 nm.

(6) an RMS in the region that 50 nm<λ (spatial wavelength)<250 nm is notmore than 0.15 nm.

Furthermore, the invention provides a glass substrate having a substratesurface that satisfies the following requirements (3) to (6) (this glasssubstrate will be hereinafter referred to as “glass substrate (4) of theinvention”).

(3) an RMS slope in the region that 2.5 μm<λ (spatial wavelength)<1 mmis not more than 0.45 mRad.

(4) an RMS slope in the region that 250 nm<λ (spatial wavelength)<2.5 μmis not more than 0.5 mRad.

(5) an RMS in the region that 100 nm<λ (spatial wavelength)<1 μm is notmore than 0.1 nm.

(6) an RMS in the region that 50 nm<λ (spatial wavelength)<250 nm is notmore than 0.15 nm.

The glass substrate (1) of the invention is preferably obtained by thefinishing method of the invention; and it is preferred that thesubstrate surface after the second finishing satisfies the foregoingrequirements (1) and (2).

The glass substrate (2) of the invention is preferably obtained by thefinishing method of the invention; and it is preferred that thesubstrate surface after the second finishing satisfies the foregoingrequirements (3) and (4).

The glass substrate (3) of the invention is preferably obtained by thefinishing method of the invention; and it is preferred that thesubstrate surface after the second finishing satisfies the foregoingrequirements (5) and (6).

The glass substrate (4) of the invention is preferably obtained by thefinishing method of the invention; and it is preferred that thesubstrate surface after the second finishing satisfies the foregoingrequirements (3) to (6).

In the glass substrates (1) to (4) of the invention, it is preferredthat the flatness of the substrate surface after the second finishing isnot more than 50 nm.

In the glass substrates (1) to (4) of the invention, it is preferredthat the RMS in a high spatial frequency (HSFR) region of the substratesurface after the second finishing is not more than 0.15 nm (RMS).

Furthermore, the invention provides a photomask blank obtained from theforegoing glass substrates (1) to (4) of the invention.

Furthermore, the invention provides a photomask obtained from theforegoing mask blank of the invention.

Furthermore, the invention provides an exposure tool using the glasssubstrate of the invention as an optical element of an optical system.

Advantages of the Invention

In the finishing method of the invention, since the flatness of theglass substrate surface after the pre-polishing and the concentrationdistribution of the dopant contained in the glass substrate aremeasured, and the processing conditions of the glass substrate surfaceare set up for each site of the glass substrate based on the measurementresults, the waviness generated on the glass substrate surface duringthe pre-polishing can be effectively removed. Furthermore, since theprocessing conditions of the glass substrate surface are set up for eachsite of the glass substrate based on the measurement results of theconcentration distribution of the dopant contained in the glasssubstrate, there is no concern that waviness is newly generated on theglass substrate surface during the finishing, or the waviness generatedduring the pre-polishing grows during the finishing. Consequently,according to the finishing method of the invention, the glass substratecan be processed so as to have a surface with an excellent flatness.

In addition, by carrying out the second finishing, the glass substratecan be processed so as to have a surface with excellent RMS slope andRMS in an HSFR region.

Since the glass substrate finished by the invention is excellent in anRMS slope, an RMS in an HSFR region and flatness, it is suitable for anoptical element of an optical system of an exposure tool, in particular,an optical element to be used in an optical system of an exposure toolfor semiconductor production of next generations having a line width of45 nm or finer, and for a photomask and a mask blank to be used for theproduction thereof, in particular, a reflective type mask for use inEUVL, and for a mask blank to be used for the production of the mask.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic configuration view showing an embodiment of ashape measurement unit which is used in the step of measuring surfaceflatness.

FIG. 2 is a graph showing correlation between dopant concentrations andprocessing rates regarding doped quartz glass containing TiO₂ as adopant.

DESCRIPTION OF REFERENCE NUMERALS AND SIGNS 10: Interferometer 10a: Pathmatch route part 10b: Interference optical system 10c: Imaging system11: Light source 12, 17: Beam splitter 12a, 17a: Half mirror surface 13,14: Mirror 15: Beam expander 16: Convergent lens 18: Collimator lens 19:Transmissive reference plate 19a: Reference plane 21: Image formationlens 22: Imaging camera 23: Uniaxial stage 24: Actuator 30: Glasssubstrate-holding unit 31: Back-plate part 32, 33: Support member 40:Glass substrate 41: Front surface 42: Back surface 50: Computer device(analyzing means) 51: Fringe image analysis unit 54: Control unit 56:Driving driver

BEST MODES FOR CARRYING OUT THE INVENTION

The finishing method of the invention is a method for finishing a glasssubstrate surface after the pre-polishing. More specifically, it is amethod in which waviness generated on the glass substrate surface duringthe pre-polishing is removed, and the glass substrate is finished so asto have a surface with excellent flatness.

The pre-polishing as referred to herein is a procedure in which a glasssubstrate surface is processed at a relatively high processing rate tosome extent of flatness and RMS in a high spatial frequency (HSFR)region before being processed to given flatness and RMS in an HSFRregion. The pre-polished glass substrate surface is finished so as tohave given flatness and RMS in an HSFR region.

The RMS in an HSFR region of the glass substrate surface after thepre-polishing is preferably not more than 5 nm, and more preferably notmore than 1 nm. The RMS in an HSFR region as referred to in thisspecification means a surface roughness in a region of a spatialwavelength of from 50 to 250 nm as measured by an atomic forcemicroscope (AFM) on an area of from 1 to 10 μm square. When the RMS inan HSFR region on the glass substrate surface after the pre-polishingexceeds 5 nm, it takes a considerably long period of time to finish theglass substrate surface by the finish polishing method of the invention,which leads to a factor of increasing the costs.

The processing method which is used for the pre-polishing is notparticularly limited and can be widely selected among known processingmethods used for processing a glass surface. In general, however, amechanical polishing method is used because it has a high processingrate, and a large area can be polished at a time by using a polishingpad having a large surface area. The mechanical polishing method asreferred to herein also includes, in addition to polishing only by apolishing action by abrasive grains, a method using a polishing slurryin which a polishing action by abrasive grains is combined with achemical polishing action by a chemical. The mechanical polishing methodmay be any of lapping and polishing, and a polishing tool and anabrasive to be used can be appropriately selected among known ones. Whena mechanical polishing method is used, for the purpose of increasing theprocessing rate, in the case of lapping, the surface pressure ispreferably from 30 to 70 gf/cm², and preferably from 40 to 60 gf/cm²;and in the case of polishing, the surface pressure is more preferablyfrom 60 to 140 gf/cm², and more preferably from 80 to 120 gf/cm². In thecase of lapping, the polishing amount is preferably from 100 to 300 μm;and in the case of polishing, the polishing amount is preferably from 1to 60 μm.

When mechanical polishing is carried out at the foregoing surfacepressure and polishing amount, waviness is generated on the glasssubstrate surface due to a rate difference by composition distributionof a substrate such as a concentration distribution of the dopantcontained in the glass substrate. However, the waviness generated on theglass substrate surface during the pre-polishing can be effectivelyremoved by the finishing method of the invention.

The waviness as referred to herein means one having periodic concavesand convexes of from 5 to 30 mm among those present on the glasssubstrate surface. The finishing method of the invention is a method ofeffectively removing the waviness generated on the glass substratesurface during the pre-polishing.

The finishing method of the invention is suitable for finishing of aglass substrate for use in an EUVL reflective type mask which canconform to the trend toward a high degree of integration and a highdefinition in an integrated circuit. The glass substrate which is usedin this application is a glass substrate having a low coefficient ofthermal expansion and a reduced fluctuation thereof. The glass substrateis preferably made of a low-expansion glass having a coefficient ofthermal expansion at 20° C. of 0±30 ppb/° C., and more preferably madeof an ultralow-expansion glass having a coefficient of thermal expansionat 20° C. of 0±10 ppb/° C.

Most widely used as such low-expansion glass and ultralow-expansionglass is quartz glass which comprises SiO₂ as a main component and towhich a dopant is added for the purpose of reducing a coefficient ofthermal expansion of glass. A typical example of the dopant to be addedfor the purpose of reducing a coefficient of thermal expansion of glassis TiO₂. Specific examples of the low-expansion glass andultralow-expansion glass to which TiO₂ is added as a dopant include ULE(a registered trademark) Code 7972 (manufactured by CorningIncorporated).

In the finishing method of the invention, the glass constituting theglass substrate is quartz glass which comprises SiO₂ as a main componentand to which a dopant is added. A typical example thereof is quartzglass to which TiO₂ is added for the purpose of reducing a coefficientof thermal expansion of glass. However, the glass constituting the glasssubstrate is not limited thereto and may be quartz glass which comprisesSiO₂ as a main component and to which a dopant is added for otherpurpose than the foregoing purpose. In this specification, quartzglasses which comprise SiO₂ as a main component and to which any dopantis added are hereinafter referred to inclusively as “doped quartzglass”.

Examples of the doped quartz glass to which a dopant is added for otherpurpose than the purpose of reducing a coefficient of thermal expansioninclude doped quartz glass to which La₂O₃, Al₂O₃, ZrO₂ or N is added forthe purpose of increasing an absolute refractive index of glass; anddoped quartz glass to which F is added for the purpose of enhancing thelaser resistance of glass.

The dopant content in the doped quartz glass varies depending on thekind of the dopant and the purpose of incorporating the dopant. In thecase of doped quartz glass to which TiO₂ is added for the purpose ofreducing a coefficient of thermal expansion of glass, it is preferredthat TiO₂ is incorporated in an amount of from 1 to 12% by mass relativeto SiO₂. When the TiO₂ content is less than 1% by mass, there is aconcern that the coefficient of thermal expansion of glass cannot besufficiently reduced. When the TiO₂ content exceeds 12% by mass, thecoefficient of thermal expansion becomes large toward the negative sideand is less than −30 ppb/° C. The TiO₂ content is more preferably from 5to 9% by mass.

So far as the waviness generated on the glass substrate surface duringthe pre-polishing can be removed by the procedures described below, thefinishing method of the invention is applicable to other glasssubstrates than those made of doped quartz glass. Consequently, thefinishing method of the invention is thought to be also applicable tolow-expansion crystallized glasses containing TiO₂ or ZrO₂ as a crystalnucleus.

The shape, size, thickness, etc. of the glass substrate are notparticularly limited. However, in the case of a substrate for use in anEUVL reflective type mask, its shape is a plate-shaped body having arectangular or square shape in terms of a planar shape.

The finishing method of the invention includes a step of measuringflatness of the glass substrate surface (hereinafter referred to as“surface flatness measurement step”) and a step of measuring aconcentration distribution of a dopant contained in the glass substrate(hereinafter referred to as “dopant concentration distributionmeasurement step”), and processing conditions of the glass substratesurface are set up for each site of the glass substrate based on theresults obtained from these steps. In this specification, setting up theprocessing conditions of the glass substrate surface for each site ofthe glass substrate are hereinafter simply referred to as “to set upprocessing conditions of the glass substrate”.

In the surface flatness measurement step, the flatness of the glasssubstrate surface is measured using a shape measurement unit providedwith a low-coherent light source whose outgoing light flux has acoherence length shorter than twice an optical distance between frontand back surfaces of the glass substrate; and a path match route partthat divides the outgoing light flux from the low-coherent light sourceinto two light fluxes, causes one of the two light fluxes to make adetour by a given optical path length relative to the other light flux,and then recombines the beams into a single light flux and outputs it.

The invention is hereunder described in detail with reference to thedrawing. FIG. 1 is a diagrammatic configuration view showing anembodiment of the shape measurement unit which is used in the surfaceflatness measurement step. The shape measurement unit shown in FIG. 1 isused for the purpose of measuring the flatness of a front surface 41 ofa glass substrate 40 in a clean room or the like and is configured toinclude an interferometer 10, a transmissive reference plate 19, a glasssubstrate-holding unit 30 and a computer device 50 serving as ananalyzing means.

The interferometer 10 is provided with a path match route part 10 a foradjusting an optical path length of a measurement beam, an interferenceoptical system 10 b for acquiring an interference fringe and an imagingsystem 10 c for imaging the acquired interference fringe. The path matchroute part 10 a is provided with a beam splitter 12 and two mirrors 13,14. A light flux output from a light source 11 is divided into two lightfluxes on a half mirror surface 12 a of the beam splitter 12. The pathmatch route part 10 a is configured such that the divided two lightfluxes are reflected in an opposite direction to each other by themirrors 13, 14 and returned to the beam splitter 12; that parts of therespective light fluxes are combined into a single light flux on thehalf mirror surface 12 a; and that the thus combined single light fluxis emitted toward the interference optical system 10 b as a measurementlight flux.

In the path match route part 10 a, the mirror 14 is held by a uniaxialstage 23 in such a manner that it is movable in the horizontal directionin the drawing. A path length difference between a reciprocating routebetween a branch point on the half minor surface 12 a and the mirror 14(this route will be hereinafter referred to as “first route”) and areciprocating route between this branch point and the mirror 13 (thisroute will be hereinafter referred to as “second route”) can be adjustedby changing the position of the mirror 14 by driving the uniaxial stage23 by an actuator 24. In the shape measurement unit shown in FIG. 1, onelight flux passing through the first route is configured so as to make adetour (traveling a longer way), by a given optical path length,relative to the other light flux passing through the second route.

The light source 11 is configured of a low-coherent light source set upsuch that a coherence length of an outgoing light flux outputted as ameasurement light flux becomes shorter than twice the optical pathlength between the front surface 41 and the back surface 42 of the glasssubstrate 40. As such a low-coherent light source, general low-coherentlight sources such as LED, SLD, halogen lamps, high mercury vaporpressure lamps, etc.; and wavelength modulation light sources which areadjusted so as to have a coherence length equivalent to the coherencelength of the low-coherent light source when an image of an interferencefringe is captured by an imaging element can be used. The wavelengthmodulation light source of this type modulates the wavelength of lightemitted from the light source (a semiconductor laser light source (LD)is usually used) within a period of time shorter than a response time ofthe imaging element (a light storage time) and images an interferencefringe in a time-averaged manner within the response time of the imagingelement, thereby obtaining a result equivalent to that achieved when alight source emitting light having a wide spectrum width and a shortcoherence length is employed. For example, a method for compositing acoherence function is described in Proceedings of Light Wave Sensing,May 1995, pages 75 to 82. Furthermore, an improved technique based onthis method is also disclosed (JP-A-2004-37165).

The interference optical system 10 b is provided with a beam expander15, a convergent lens 16, a beam splitter 17 and a collimator lens 18,which are arranged in sequence of propagation of the measurement lightflux emitted from the path match route part 10 a. The imaging system 10c is provided with an image formation lens 21 and an imaging camera 22,which are disposed below the beam splitter 17 in the drawing.Furthermore, the interference optical system 10 b configures a Fizeautype optical system disposition along with the transmissive referenceplate 19. An interference fringe which is formed from reference lightreflected from a reference plane 19 a of the transmissive referenceplate 19 and light returning from the glass substrate 40 aftertransmitting through the reference plane 19 a is formed into an image onan imaging element such as CCD, CMOS, etc. in the imaging camera 22 viaa half mirror face 17 a of the beam splitter 17 and the image formationlens 21.

Although not illustrated, the transmissive reference plate 19 isprovided with a fringe scan adapter for accomplishing fine motion of thetransmissive reference plate 19 in the direction of an optical axis Lwhen fringe scan measurement is performed; and a tilt adjustmentmechanism for finely adjusting an inclination of the glass substrate 40held by the glass substrate-holding unit 30 with respect to thereference plane 19 a.

The glass substrate-holding unit 30 is provided with a back-plate part31 and a pair of upper and lower support members 32, 33 for supportingthe glass substrate 40 fixed to the back-plate part 31.

The support members 32, 33 are configured so as to vertically come intocontact with the glass substrate 40 from the both sides with a normalline of the plane of the glass substrate 40 interposed therebetween (thenormal line being coincident with an optical axis L in FIG. 1) and thushold the glass substrate 40 such that the normal line of the planebecomes substantially perpendicular to the direction of gravity(horizontal direction in the drawing).

Although illustration is omitted, the support members 32, 33 areprovided with press members which are provided in positions in thevicinity of the front or back surface or side surface of the glasssubstrate 40 for preventing tilting of the glass substrate 40. Amaterial which less likely generates dusts, for example, a PEEK material(PEEK: polyetheretherketone), etc., is preferably used for the supportmembers 32, 33 and the press members.

Furthermore, as shown in FIG. 1, the computer device 50 is provided witha fringe image analysis unit 51 which is configured of a microprocessor,various memory devices, arithmetic processing programs stored in thememory devices, etc. and a control unit 54 and also connected with amonitor device for displaying the obtained interference fringe image,etc. and an input device for effecting input operations with respect tothe computer device 50 (all of which are not illustrated). The controlunit 54 is configured so as to adjust the position of the mirror 14 bycontrolling the driving amount of the actuator 24 via the driving driver56.

Procedures for measuring the flatness of the front surface 41 of theglass substrate 40 using the shape measurement unit shown in FIG. 1 arehereunder described.

First, by using the glass substrate-holding unit 30, a pair of thesupport members 32, 33 is brought into contact with the glass substrate40 from the both vertical sides thereof with the normal line of theplane of the glass substrate 40 interposed therebetween, therebyarranging the glass substrate 40 such that the normal line of the planebecomes essentially perpendicular to the direction of gravity. At thattime, adjustment is performed by using a non-illustrated tilt adjustmentmechanism such that the reference plane 19 a of the transmissivereference plate 19 and the front surface 41 of the glass substrate 40become essentially parallel to each other.

Next, the flatness of the front surface 41 of the glass substrate 40held by the support members 32, 33 is measured using the interferometer10 and the computer device 50 shown in FIG. 1. The flatness of the glasssubstrate surface as referred to herein means the flatness of each siteof the glass substrate surface, namely a difference in height.Consequently, the measurement results serve as a flatness map showing adifference in height in each site of the glass substrate surface(hereinafter referred to as “flatness map”).

In measuring the flatness of the front surface 41 of the glass substrate40 using the interferometer 10 and the computer device 50 shown in FIG.1, adjustment of the route length of the measurement light flux isperformed in the path match route part 10, thereby eliminating theinterference by the light reflected from the back surface 42 of theglass substrate 40.

The light returning from the glass substrate 40 to the reference plane19 a includes first returning light which is reflected on the frontsurface 41 of the glass substrate 40 after transmitting through thisreference plane 19 a and second returning light which is reflected onthe back surface 42 after entering the inside of the glass substrate 40from this front surface 41.

Since the front surface 41 of the glass substrate 40 is the surface tobe measured in the measurement of the flatness of the glass substratesurface, what is required is information of an interference fringeresulting from interference between the first returning light and thereference light. When interference by light which is reflected from theback surface 42 of the glass substrate 40, namely, interference betweenthe reference light and the second returning light, or interferencebetween the first returning light and the second returning light, isgenerated, such interference becomes a noise and adversely affects theaccuracy of measurement.

In the surface flatness measurement step, by performing adjustment ofthe route length of the measurement light flux in the path match routepart 10 a, interference by the light which is reflected from the backsurface 42 of the glass substrate 40 is eliminated. Specifically, theadjustment is performed such that the optical path length differencebetween the first route and the second route coincides with the opticalpath length difference between the reference light and the firstreturning light in the interference optical system 10 b, within therange of the coherence length of the light source 11. As a result, onlythe required interference is generated, and unnecessary interference iseliminated.

Since adverse effects by the reflection on the back surface of thesubstrate are eliminated, the flatness of the glass substrate surfacecan be measured with high accuracy in the surface flatness measurementstep.

Moreover, in the interferometer 10 shown in FIG. 1, a distance betweenthe reference plane 19 a of the transmissive reference plate 19 and thefront surface 41 of the glass substrate 40 may be small whatever it maybe, so far as the both do not come into contact with each other, and,for example, the distance between the both may be in a sub-millimeterorder. Consequently, the influence by air fluctuation as in the methoddisclosed in Patent Document 3 can be neglected.

In measuring the flatness of the glass substrate surface by the shapemeasurement unit shown in FIG. 1, a holding distortion by the glasssubstrate-holding unit 30 is formed in the glass substrate 40. However,since the glass substrate 40 is held at a controlled extremely lowpressure, the influence against the accuracy of measurement by theholding distortion is very small, and hence, it can be generallyneglected.

However, in the case where the requirements regarding the flatnessbecome severer, there is a possibility that the influence against theaccuracy of measurement by the holding distortion cannot be neglected.In that case, by measuring the flatness of the glass substrate surfaceby the following procedures, the flatness of a glass substrate surfacein a state free from a holding distortion can be determined.

(a) The flatness of the front surface 41 of the glass substrate 40 ismeasured using information about an interference fringe generated by thefirst returning light and the reference light.

(b) The glass substrate 40 is turned over upside down, namely, the glasssubstrate 40 is held by the glass substrate-holding unit 30 such thatthe back surface 42 is located on the side of the transmissive referenceplate 19, and the flatness of the front surface 41 of the glasssubstrate 40 is measured using information about an interference fringegenerated by the second returning light which, after entering the insideof the glass substrate 40 from the back surface 42, is reflected on thefront surface 41 and the reference light.

(c) The holding distortion of the glass substrate 40 is determined fromthe measurement results obtained in (a) and (b).

(d) The flatness of the front surface 41 of the glass substrate 40 in astate free from a holding distortion is determined from the holdingdistortion obtained in (c) and the measurement results obtained in (a).

In the case of carrying out the dopant concentration distributionmeasurement step, correlation between the concentration of the dopantcontained in the glass substrate and the processing rate of the glasssubstrate surface is determined beforehand (hereinafter referred to as“correlation between dopant concentration and processing rate”).

The present inventors have found that when a glass substrate made ofdoped quartz glass is processed, there is some correlation between thedopant concentration and the processing rate.

For example, in the case of doped quartz glass containing TiO₂ as adopant, when the doped quartz glass is processed under constantprocessing conditions, there is the correlation represented by thefollowing equation (1) between the dopant concentration X (wt %) and theprocessing rate Y (μm/min).Y=a·X+b  (1)

In the equation (1), a and b each represents a variable.

FIG. 2 is a graph showing the correlation between dopant concentrationand processing rate regarding doped quartz glass containing TiO₂ as adopant, and shows the correlation in the case of using gas cluster ionbeam etching as a processing method. The procedures used for preparingFIG. 2 are shown below.

Test samples (20 mm×20 mm×1 mm in thickness) made of doped quartz glasscontaining TiO₂ in an amount of 0%, 3.1%, 5.1%, 6.9% and 8.7%,respectively, in terms of % by mass relative to SiO₂ were prepared.These test samples having a different TiO₂ concentration from each otherwere processed under the same conditions, thereby determining aprocessing rate. A graph obtained by plotting the relationship betweenthe TiO₂ concentration and the processing rate is FIG. 2. In FIG. 2, theprocessing rate is shown as a normalized processing rate whileexpressing the processing rate at a TiO₂ concentration of 0% by mass as1.

The gas cluster ion beam etching was carried out under the followingconditions.

Source gas: SF₆ 1.25%, O₂ 24%, Ar 74.75%

Accelerating voltage: 30 kV

Ionizing current: 50 μA

Beam diameter (FWHM value): not more than 10 mm

Dose: 6.2×10¹⁵ ions/cm²

The processing rate shown in FIG. 2 was determined from a weight changeof the test sample before and after the processing by a gravimetricmethod.

When the gas cluster ion beam etching is carried out under the foregoingprocessing conditions, then the foregoing equation (1) is determined asthe following equation (1-1) from FIG. 2.Y=0.0522X+1.0449  (1-1)

Consequently, the correlation between dopant concentration andprocessing rate can be determined by preparing plural glass samples inwhich the glass substrate to be finished in the invention, the matrixcomponent and the kind of the dopant are identical but the dopantconcentration is varied; processing these plural glass samples under thesame processing conditions; and preparing a graph the same as in FIG. 2.

Next, the following procedures are carried out.

(1) The flatness of the glass substrate surface is measured.

(2) The glass substrate surface is processed in a given amount underconstant processing conditions.

(3) The flatness of the glass substrate surface after the processing ismeasured.

Here, the procedure (1) may be the same as the foregoing surfaceflatness measurement step. For the purpose of decreasing the stepnumber, it is rather preferred that the procedure (1) is the same as thesurface flatness measurement step.

In the procedure (2), the glass substrate surface is uniformly processedunder the constant processing conditions using the processing methodwhich is used in determining the correlation between dopantconcentration and processing rate. Here, it is preferred that theprocessing conditions are the same as the processing conditions whichare used in determining the correlation between dopant concentration andprocessing rate. For example, in the case where the processing method isgas cluster ion beam etching, it is preferred that the processing iscarried out using the same source gas at the same dose.

The processing which is carried out in the procedure (2) is made for thepurpose of measuring the concentration distribution of the dopantcontained in the glass substrate and differs from the finishing of theglass substrate surface. Consequently, in order to secure a sufficientprocessing amount at the time of finishing, it is preferred that theprocessing amount at which the processing is carried out in theprocedure (2) is a processing amount of the necessary minimum formeasuring the concentration distribution of the dopant. For example, theprocessing amount at which the processing is carried out in theprocedure (2) is preferably not more than 5,000 nm, more preferably notmore than 2,000 nm, and especially preferably not more than 100 nm.

In the procedure (3), it is preferred that the measurement of theflatness of the glass substrate surface is carried out using the shapemeasurement unit shown in FIG. 1 because the flatness of the glasssubstrate surface can be measured with high accuracy.

Next, the distribution of processing amount of the glass substrate isdetermined from a difference in the flatness before and after theprocessing. That is, the processing amount in each site of the glasssubstrate is determined from a difference in the flatness obtained inthe procedures (1) and (3).

Since the glass substrate is uniformly processed under constantprocessing conditions, the concentration distribution of the dopantcontained in the glass substrate can be determined by comparing theprocessing amount in each site of the glass substrate with thecorrelation between dopant concentration and processing rate, which hasbeen determined beforehand. However, since the substrate surface whoseflatness is to be measured in the procedure (1) is usually not smoothand has concaves and convexes to some extent, an actual processingamount in each part of the glass substrate cannot be determined from adifference in the flatness obtained in the procedures (1) and (3). Forthat reason, while expressing an average value of the processing amount(nominal) in each part of the glass substrate determined from adifference in the flatness obtained in the procedures (1) and (3) as aconcentration center of the dopant, the concentration distribution ofthe dopant contained in the glass substrate is determined as a deviationfrom the concentration center. Here, the concentration center can bemade as a target value of the doping amount in a synthesis step of theglass substrate. The concentration center may be corrected by measuringthe mass of the glass substrate before and after the processing,determining an actual processing amount from a mass change before andafter the processing and using the obtained actual processing amount. Asthe case may be, the dopant concentration distribution may be corrected.

In the dopant concentration distribution measurement step, theconcentration distribution of the dopant contained in the glasssubstrate, as referred to herein, does not mean the concentrationdistribution of the dopant in a thickness direction of the glasssubstrate, but it means, regarding a plate-shaped glass substrate asbeing of a two-dimensional shape having no thickness, the concentrationdistribution of the dopant in each site of the two-dimensional shape,namely, the concentration distribution in a plane of the plate-shapedglass substrate. The dopant concentration distribution in a planeparallel to the glass substrate in an arbitrary thickness of the glasssubstrate is supposed to be equal to the concentration distribution ofthe measured surface of the glass substrate.

Consequently, the measurement results obtained from the dopantconcentration distribution measurement step serve as a dopantconcentration distribution map showing the concentration of the dopantin each site of the two-dimensional shape (hereinafter referred to as“dopant concentration distribution map”).

In the finishing method of the invention, the processing conditions ofthe glass substrate surface are set up based on both of the resultsobtained from the surface flatness measurement step and the resultsobtained from the dopant concentration distribution measurement step.However, for the sake of facilitating understanding, the descriptionwill be made while dividing it into the setting of the processingconditions based on the results obtained from the surface flatnessmeasurement step and the setting of the processing conditions based onthe results obtained from the dopant concentration distributionmeasurement step.

As described above, the results obtained from the surface flatnessmeasurement step serve as a flatness map showing a difference in heightin each site of the glass substrate surface. In a glass substrate of atwo-dimensional shape having no thickness, which is the conception usedwith regard to the dopant concentration distribution, when coordinatesfor the glass substrate are expressed as (x,y), the flatness map isexpressed as S(x,y) (μm). When the processing time and processing rateof the glass substrate are expressed as T(x,y) (min) and Y (μm/min),respectively, then the relationship therebetween is expressed by thefollowing equation (2).T(x,y)=S(x,y)/Y  (2)

Consequently, in setting up the processing conditions based on theresults obtained from the surface flatness measurement step, theprocessing conditions, specifically the processing time, is set upaccording to the equation (2).

On the other hand, the results obtained from the dopant concentrationdistribution measurement step serve as a dopant concentrationdistribution map showing the concentration of the dopant in each site ofthe glass substrate. In a glass substrate of a two-dimensional shapehaving no thickness, which is the conception used with regard to thedopant concentration distribution, when coordinates for the glasssubstrate are expressed as (x,y), the dopant concentration distributionmap obtained from the dopant concentration measure step is expressed asC(x,y) (% by mass). When the processing amount and processing time ofthe glass substrate are expressed as W(x,y) (μm/min) and T(x,y) (min),respectively, then the relationship between W(x,y) and T(x,y) isexpressed by the following equation (3).T(x,y)=W(x,y)/(a×C(x,y)+b)  (3)

W(x,Y) represents a processing amount (predetermined processing amount)of the site of the coordinates (x,y) of the glass substrate and is aconstant. For example, when the site of the coordinates (x,y) of theglass substrate is processed in an amount of 5 μm, then W(x,Y) is 5 μn.

Consequently, in setting up the processing conditions of the glasssubstrate based on the results obtained from the dopant concentrationdistribution measurement step, the processing conditions of the glasssubstrate, specifically the processing time, may be set up according tothe equation (3).

In the case where the processing conditions of the glass substratesurface are set up based on both of the results obtained from thesurface flatness measurement step and the results obtained from thedopant concentration distribution measurement step, when the coordinatesof the glass substrate of a two-dimensional shape, the flatness mapobtained from the surface flatness measurement step, the dopantconcentration distribution map obtained from the dopant concentrationdistribution measurement step and the processing time are expressed as(x,y), S(x,y) (μm), C(x,y) (% by mass) and T(x,y) (min), respectively,then the relationship among them is expressed by the following equation(4).T(x,y)=S(x,y)/(a×C(x,y)+b)  (4)

Consequently, in setting up the processing conditions based on both ofthe results obtained from the surface flatness measurement step and theresults obtained from the dopant concentration distribution measurementstep, the processing conditions of the glass substrate, specifically theprocessing time, is set up according to the equation (4).

With regard to the processing method which is used in the processingmethod of the invention, any one of the processing methods selected fromthe group consisting of ion beam etching, gas cluster ion beam etchingand plasma etching is used, because it can make the range to beprocessed by one processing operation sufficiently small, and becausethe processing conditions can be easily set up based on the results inthe surface flatness measurement step and the dopant concentrationdistribution measurement step, for example, it is easy to set up theprocessing time according to the equation (4). In these methodsaccompanied with irradiation with a beam onto the glass substratesurface, the energy of a beam to be irradiated onto the glass substratesurface is stable, and even when the energy of a beam fluctuates, theenergy of the beam can be confirmed through monitoring. Consequently,there is brought an advantage that the processing can be always achievedunder intended processing conditions.

In carrying out such a processing method accompanied with irradiationwith a beam onto the glass substrate surface, an angle formed by thenormal line of the glass substrate and an incident beam onto the glasssubstrate surface is kept at from 30 to 89°. When the angle formed bythe normal line of the glass substrate and an incident beam onto theglass substrate surface is 30° or more, the reactivity between thesubstrate and the beam becomes weak so that it is possible to control anRMS at a shorter wavelength. For this reason, an RMS in an HSFR regionof the glass substrate and an RMS slope at a wavelength of from 50 nm to1 mm can be improved. In the case where the foregoing angle is largerthan 89°, it is difficult to control the incident beam onto the glasssurface, and hence, such is not preferred.

The angle formed by the normal line of the glass substrate and anincident beam onto the glass substrate surface is more preferably from50 to 85°, and especially preferably from 60 to 80°.

In such a processing method accompanied with irradiation with a beamonto the glass substrate surface, the processing conditions of the glasssubstrate can be further set up based on the results obtained from thesurface flatness measurement step. The procedure of the settings ishereunder specifically described.

In conducting this setting procedure, the results obtained from thesurface flatness measurement step are used to specify the width ofwaviness present on the glass substrate surface. The width of wavinessas referred to herein means a length of a concave or a convex in theshape with concaves and convexes present periodically on the glasssubstrate surface. Consequently, the width of waviness is generallyone-half the period of the waviness. In the case where the plural ofwaviness having a different period from each other is present on theglass substrate surface, the width of the waviness having the shortestperiod is taken as the width of waviness present on the glass substratesurface.

As described above, the measurement results obtained from the surfaceflatness measurement step serve as a flatness map showing a differencein height in each site of the glass substrate surface. Consequently, thewidth of waviness present on the glass substrate surface can be easilyspecified from the flatness map.

By making the width of waviness specified by the foregoing procedure asa reference, dry etching is carried out using a beam having a beamdiameter not more than the width of waviness. Here, the beam diameter ismade based on an FWHM (full width of half maximum) value. The beamdiameter as referred to in this specification means an FWHM value of thebeam diameter. In the finishing method of the invention, it is morepreferred to use a beam having a beam diameter not more than one-halfthe width of waviness. When a beam having a beam diameter not more thanthe width of waviness is used, the beam can be concentratedly irradiatedon the waviness present on the surface of the glass substrate, and thewaviness can be effectively removed.

In carrying out such a processing method accompanied with irradiationwith a beam, it is necessary to scan the beam on the surface of theglass substrate. This is because for the purpose of setting up theprocessing conditions of the glass substrate, it is necessary to makethe range to be irradiated with a beam in one operation small as far aspossible. In particular, when a beam having a beam diameter not morethan the width of waviness is used, it is necessary to scan the beam onthe surface of the glass substrate. As a method of scanning a beam,raster scanning and spiral scanning are known, and any of them may beused.

In the finish polishing method of the invention, in the case where theprocessing time (irradiation time of a beam in this case) is set upaccording to the foregoing equation (4), the settings are conducted soas to obtain an irradiation time T(x,y) at the coordinates (x,y). Thatis, the settings are conducted so as to obtain an irradiation timeT(x,y) set up by determining a relative movement speed between the glasssubstrate and the beam while taking into consideration a beam intensityprofile, a scanning pitch and a dose.

Among the methods accompanied with irradiation with a beam onto theglass substrate surface, it is preferred to use gas cluster ion beametching because the surface can be processed so as to have a smallsurface roughness and excellent smoothness.

The gas cluster ion beam etching as referred to herein is a method inwhich a reactive material (source gas) which is in a gaseous form atnormal temperature and normal pressure is injected in a compressed stateinto a vacuum apparatus through an expansion type nozzle, therebyforming a gas cluster, which is then ionized upon irradiation with anelectron to form a gas cluster ion beam, and the gas cluster ion beam isirradiated on an object, thereby etching an object. The gas cluster isgenerally constituted of a block-shaped atomic or molecular aggregatecomposed of several thousand atoms or molecules. In the processingmethod of the invention, in the case where gas cluster ion beam etchingis used, when the gas cluster collides with the glass substrate surface,a multi-body collision effect is caused due to an interaction with thesolid, whereby the glass substrate surface is processed.

When gas cluster ion beam etching is used, a gas such as SF₆, Ar, O₂,N₂, NF₃, N₂O, CHF₃, CF₄, C₂F₆, C₃F₈, C₄F₆, SiF₄, COF₂, etc. can be usedsingly or in admixture as a source gas. Of these, SF₆ and NF₃ areexcellent as the source gas from the standpoint of a chemical reactionoccurring at the time of colliding with the glass substrate surface, andtherefore, a mixed gas containing SF₆ or NF₃ is preferred.

Specifically, a mixed gas of SF₆ and O₂, a mixed gas of SF₆, Ar and O₂,a mixed gas of NF₃ and O₂, a mixed gas of NF₃, Ar and O₂, a mixed gas ofNF₃ and N₂ and a mixed gas of NF₃, Ar and N₂ are preferred. In thesemixed gases, though a suitable mixing proportion of the respectivecomponents varies depending on conditions such as irradiationconditions, etc., the following are preferred, respectively.

SF₆/O₂=0.1 to 5%/95 to 99.9% (a mixed gas of SF₆ and O₂)

SF₆/Ar/O₂=0.1 to 5%/9.9 to 49.9%/50 to 90% (a mixed gas of SF₆, Ar andO₂)

NF₃/O₂=0.1 to 5%/95 to 99.9% (a mixed gas of NF₃ and O₂)

NF₃/Ar/O₂=0.1 to 5%/9.9 to 49.9%/50 to 90% (a mixed gas of NF₃, Ar andO₂)

NF₃/N₂=0.1 to 5%/95 to 99.9% (a mixed gas of NF₃ and N₂)

NF₃/Ar/N₂=0.1 to 5%/9.9 to 49.9%/50 to 90% (a mixed gas of NF₃, Ar andN₂)

Irradiation conditions such as a cluster size, an ionizing current to beapplied to an ionizing electrode of a gas cluster ion beam etchingapparatus for ionizing the cluster, an accelerating voltage to beapplied to an accelerating electrode of a gas cluster ion beam etchingapparatus and a dose of a gas cluster ion beam can be properly selectedaccording to the kind of the source gas and surface properties of theglass substrate after the pre-polishing. For example, for the purpose ofremoving waviness from the glass substrate surface to improve theflatness without excessively deteriorating the surface roughness of theglass substrate, it is preferred that the accelerating voltage to beapplied to the accelerating electrode is from 15 to 30 kV.

In order to increase a driving force for the physical material removal,it is preferred that a beam current is from 80 to 200 μA.

In the finishing method of the invention, since the processingconditions of the glass substrate are set up based on the resultsobtained from the surface flatness measurement step and the dopantconcentration distribution measurement step, the waviness generated onthe glass substrate surface at the time of pre-polishing can beeffectively removed, and the glass substrate can be processed into asurface having excellent flatness. When the finishing method of theinvention is used, the flatness of the glass substrate surface can beimproved to not more than 50 nm.

When the finishing method of the glass substrate surface is carried outaccording to the foregoing procedures, there may be the case where anRMS in an HSFR region of the glass substrate surface is slightlydeteriorated depending on the surface properties of the glass to beprocessed or the irradiation conditions with a beam. Furthermore,depending upon the specifications of the glass substrate, there may bethe case where, though a desired flatness can be attained, the glasssubstrate surface cannot be processed to a desired RMS in an HSFR regionaccording to the foregoing procedures.

Furthermore, there may be the case where a convex defect or a concavedefect with a diameter of about 30 nm is present on the substratesurface after the finishing according to the foregoing procedures, andit is preferred that such a convex defect or concave defect is removed.

For that reason, in the finishing method of the invention, it ispreferred that second finishing for improving an RMS in a high spatialfrequency (HSFR) region of the glass substrate surface is furthercarried out. Here, it is preferred that the second finishing is able toreduce the RMS in an HSFR region of the glass substrate surface to notmore than 0.15 nm.

With respect to the second finishing, gas cluster ion beam etching canbe used. In that case, the gas cluster ion beam etching is carried outdifferent from the foregoing gas cluster ion beam etching which is aimedto remove the waviness generated during the pre-polishing, whilealtering the irradiation conditions such as a source gas, an ionizingcurrent and an accelerating voltage. Specifically, the gas cluster ionbeam etching is carried out under milder conditions using a lowerionizing current or a lower accelerating voltage. More specifically, theaccelerating voltage is preferably 3 kV or more and less than 30 kV, andmore preferably from 3 to 20 kV. Furthermore, it is preferred to use, asa source gas, an O₂ single gas or a mixed gas of O₂ and at least one gasselected from the group consisting of Ar, CO and CO₂ because such a gashardly causes a chemical reaction at the time of colliding with thesurface of the glass substrate. Of these, it is preferred to use a mixedgas of O₂ and Ar.

In the case of carrying out gas cluster ion beam etching as the secondfinishing, for the same reasons as described above, an angle formed bythe normal line of the glass substrate and an incident beam onto theglass substrate surface is kept at from 30 to 89°. The angle formed bythe normal line of the glass substrate and an incident beam onto theglass substrate surface is more preferably from 50 to 85°, andespecially preferably from 60 to 80°.

Furthermore, mechanical polishing using a polishing slurry at a lowsurface pressure, specifically at a surface pressure of from 1 to 60g_(f)/cm², and preferably from 30 to 60 g_(f)/cm², which is called touchpolishing, can be carried out as the foregoing second finishing. In thetouch polishing, a glass substrate is set interposed by polishing discsprovided with a polishing pad such as a non-woven fabric, a polishingcloth, etc., and the polishing discs are relatively rotated with respectto the glass substrate while feeding a slurry having been adjusted so asto have given properties, thereby achieving polishing at a surfacepressure of from 1 to 60 g_(f)/cm², and preferably from 30 to 60g_(f)/cm².

In the case of carrying out touch polishing as the second finishing, inaddition to an improvement of the RMS in an HSFR region, a convex defector a concave defect with a diameter of about 30 nm, which is present onthe substrate surface, can be removed.

For example, Bellatrix K7512, manufactured by Kanebo, Ltd. is used asthe polishing pad. It is preferred to use a polishing slurry containingcolloidal silica as the polishing slurry. It is more preferred to use apolishing slurry containing colloidal silica with an average primaryparticle size of not more than 50 nm and water and having been adjustedat a pH in the range of from 0.5 to 4. The surface pressure of polishingis from 1 to 60 g_(f)/cm², and preferably from 30 to 60 g_(f)/cm². Whenthe surface pressure exceeds 60 g_(f)/cm², the RMS in an HSFR region ofthe glass substrate surface cannot be reduced to not more than 0.15 nmdue to the generation of scratches on the substrate surface or the like.Furthermore, there is a concern that a rotation load of the polishingdisc becomes large. When the surface pressure is less than 1 g_(f)/cm²,it takes a long period of time to achieve processing, and hence, such isnot practically useful.

The average primary particle size of colloidal silica is more preferablyless than 20 nm, and especially preferably less than 15 nm. Though alower limit of the average primary particle size of colloidal silica isnot specified, it is preferably 5 nm or more, and more preferably 10 nmor more from the viewpoint of enhancing the polishing efficiency. Whenthe average primary particle size of colloidal silica exceeds 50 nm, itis difficult to reduce the RMS in an HSFR region of the glass substratesurface to not more than 0.15 nm. Furthermore, from the viewpoint ofpainstakingly controlling the particle size, it is desirable that asecondary particle formed upon cohesion of the primary particle is notcontained as far as possible. Even in the case of containing a secondaryparticle, it is preferred that its average particle size is not morethan 70 nm. The particle size of colloidal silica as referred to hereinis one obtained by measuring an image with a magnification of from 15 to105×10³ using SEM (scanning electron microscope).

It is preferred that the content of colloidal silica in the polishingslurry is from 10 to 30% by mass. When the content of colloidal silicain the polishing slurry is less than 10% by mass, there is a concernthat the polishing efficiency is so poor that economical polishing isnot obtained. On the other hand, when the content of colloidal silicaexceeds 30% by mass, the use amount of colloidal silica increases, andtherefore, there is a concern that a hindrance is caused from theviewpoints of costs and cleaning properties. The content of colloidalsilica is more preferably from 18 to 25% by mass, and especiallypreferably from 18 to 22% by mass.

When the pH of the polishing slurry falls within an acidic range, namelythe pH is in the range of from 0.5 to 4, it is possible to chemicallyand mechanically polish the surface of the glass substrate, therebyefficiently polishing the glass substrate with good smoothness. That is,since convexes of the glass surface are softened by the acid of thepolishing slurry, the convexes can be easily removed by mechanicalpolishing. As a result, not only the polishing efficiency is enhanced,but glass scum removed by polishing is softened, and therefore, thegeneration of new scratches by the glass scum, etc. is prevented. Whenthe pH of the polishing slurry is less than 0.5, there is a concern thatcorrosion of a polishing device to be used for the touch polishing isgenerated. From the viewpoint of handling properties of the polishingslurry, the pH is preferably 1 or more. In order to sufficiently obtaina chemical polishing effect, the pH is preferably not more than 4, andthe pH is especially preferably in the range of from 1.8 to 2.5.

The pH adjustment of the polishing slurry can be conducted by theaddition of an inorganic acid or an organic acid singly or incombination. Examples of the inorganic acid which can be used includenitric acid, sulfuric acid, hydrochloric acid, perchloric acid,phosphoric acid, etc., with nitric acid being preferred from thestandpoint of easiness of handling. Furthermore, examples of the organicacid include oxalic acid, citric acid, etc.

With regard to water to be used in the polishing slurry, pure water orultrapure water from which foreign matters have been removed ispreferably used. That is, pure water or ultrapure water in which thenumber of a fine particle having a maximum size, as measured by a lightscattering system using laser light, etc., of 0.1 μm or more issubstantially not more than one per mL is preferred. When foreignmatters are incorporated in an amount of more than one per mL regardlessof the quality or shape, there is a concern that a surface defect suchas a scratch, a pit, etc. is generated on the polished surface. Thoughforeign matters in pure water or ultrapure water can be removed by, forexample, filtration or ultrafiltration by a membrane filter, the removalmethod of foreign matters is not limited thereto.

In the case of using any of gas cluster ion beam etching or touchpolishing, in order to reduce the RMS in an HSFR region of the glasssubstrate surface to not more than 0.15 nm, it is preferred that theprocessing amount in the second finishing is from 10 to 200 nm.

When the processing amount in the second finishing is less than 10 nm,an action to improve the RMS in an HSFR region of the glass substratesurface is insufficient. Furthermore, in the case of using touchpolishing, a convex defect and a concave defect present on the substratesurface cannot be sufficiently removed. When the processing amountexceeds 200 nm, though the RMS in an HSFR region of the glass substratesurface can be improved, there is a concern that the flatness of thesubstrate surface is deteriorated.

The glass substrate after carrying out the foregoing second finishing isespecially excellent in surface properties. Specifically, it satisfiesthe following requirements (1) and (2).

(1) an RMS slope in the region that 5 μm<λ (spatial wavelength)<1 mm isnot more than 0.5 mRad.

(2) an RMS slope in the region that 250 nm<λ (spatial wavelength)<5 μmis not more than 0.6 mRad.

The RMS slope and a method of determining it are described in thefollowing document.

Eric Gullikson, et al., “Proposed Specification of EUVL mask substrateroughness”, 2nd International EUVL Symposium, Oct. 10, 2003

The RMS slope in the region that 5 μm<λ (spatial wavelength)<1 mm can becalculated from the results obtained by measuring an area of 10 μMsquare by AFM. Similarly, the RMS slope in the region that 250 nm<λ(spatial wavelength)<5 μm can be calculated from the measurementresults, for example, under the following conditions using Zygo New View5000 Series (Zygo Corporation).

Intermediate magnification: ×1

Objective lens: ×2.5

It is preferred that the glass substrate after carrying out theforegoing second finishing satisfies the following requirements (3) and(4).

(3) an RMS slope in the region that 2.5 μm<λ (spatial wavelength)<1 mmis not more than 0.45 mRad.

(4) an RMS slope in the region that 250 nm<λ (spatial wavelength)<2.5 μmis not more than 0.5 mRad.

The RMS slope in the region that 2.5 μm<λ (spatial wavelength)<1 mm canbe calculated from the results obtained by measuring an area of 10 μmsquare by AFM. Similarly, the RMS slope in the region that 250 nm<λ(spatial wavelength)<2.5 can be calculated from the measurement results,for example, under the following conditions using Zygo New View 5000Series (Zygo Corporation).

Intermediate magnification: ×1

Objective lens: ×2.5 Furthermore, it is preferred that the glasssubstrate after carrying out the foregoing second finishing satisfiesthe following requirements (5) and (6).

(5) an RMS in the region that 100 nm<λ (spatial wavelength)<1 μm is notmore than 0.1 nm.

(6) an RMS in the region that 50 nm<λ (spatial wavelength)<250 nm is notmore than 0.15 nm.

The RMS in the region that 100 nm<λ (spatial wavelength)<1 μm and theRMS in the region that 50 nm<λ (spatial wavelength)<250 nm can becalculated from the measurement results, for example, under thefollowing conditions using Zygo New View 5000 Series (Zygo Corporation).

Intermediate magnification: ×1

Objective lens: ×2.5

It is more preferred that the glass substrate after carrying out theforegoing second finishing satisfies the foregoing requirements (3) to(6).

Furthermore, the glass substrate after the second finishing is alsoexcellent in flatness and RMS in an HSFR region. Specifically, the glasssubstrate surface has flatness of not more than 50 nm and an RMS in anHSFR region of not more than 0.15 nm.

The glass substrate finished by the method of the invention is suitableas an optical element which is used in an optical system of an exposuretool for semiconductor production, in particular, an optical elementwhich is used in an optical system of an exposure tool for semiconductorproduction of next generations having a line width of 45 nm and finer.Specific examples of such an optical element include lenses, diffractiongratings, optical membranes and complexes thereof, for example, lenses,multi-function lenses, lens arrays, lenticular lenses, fly eye lenses,non-spherical lenses, mirrors, diffraction gratings, binary opticselements, photomasks and complexes thereof.

Furthermore, the glass substrate finished by the method of the inventionis especially excellent in surface properties, and therefore, it issuitable as a photomask and a mask blank for producing the photomask, inparticular, a reflective type mask for use in UEVL and a mask blank forproducing the mask.

The light source of the exposure tool is not particularly limited andmay be a laser emitting g-line (wavelength: 436 nm) or i-line(wavelength: 365 nm) heretofore in use. However, light sources with ashorter wavelength, specifically light sources having a wavelength ofnot more than 250 nm are preferred. Specific examples of such a lightsource include a KrF excimer laser (wavelength: 248 nm), an ArF excimerlaser (wavelength: 193 nm), an F₂ laser (wavelength: 157 nm) and EUV(13.5 nm).

EXAMPLES

The invention will be more specifically described below with referenceto the following Examples, but it should not be construed that theinvention is limited thereto. Examples 1 to 5 and Examples 7 to 11 areinvention examples, and Examples 6 and 12 are comparative examples.

As a material to be polished, an ingot of TiO₂-doped synthetic quartzglass which was produced by a known method, was cut into a plate shapehaving a size of 153.0 mm in length×153.0 mm in width and 6.75 mm inthickness, thereby preparing a plate sample made of Ti-doped syntheticquartz glass. Subsequently, the sample was beveled with an NC bevelingmachine so as to have an outer dimension of 152 nm and a bevel width offrom 0.2 to 0.4 mm.

The foregoing plate sample was polished using a double-sided lappingmachine until the thickness reached 6.51 mm, and an outer peripherythereof was then polished using a buff, thereby achieving end-facemirror finishing.

Subsequently, the resulting plate material was subjected to primarypolishing using a double-sided polishing machine. The plate samplehaving been mechanically polished according to the foregoing procedureswas subjected to simple cleaning and precise cleaning. Thereafter, theflatness of the plate sample was measured with a flatness analyzer.

This flatness analyzer is provided with a light source, a path matchroute part and an interference optical system. With respect to the lightsource, its outgoing light flux has a coherence length shorter thantwice an optical distance between front and back surfaces of the glasssubstrate. The path match route part divides the outgoing light fluxfrom the light source into two light fluxes, causes one of the two lightfluxes to make a detour, by a given optical path length, relative to theother of the two light fluxes, and then recombines the light fluxes intoa single light flux and outputs it. The interference optical systemacquires an interference fringe which carries wave surface informationof the glass substrate surface by radiating the outgoing light flux fromthe light source onto a reference surface and the glass substratesurface held on a measurement optical axis and making lights returningfrom the reference surface and the glass substrate surface interferewith each other.

As a result of the measurement by the foregoing flatness analyzer, theflatness of the surface of the plate sample was found to be 337 nm/142mm square.

Furthermore, the surface roughness of the foregoing plate sample wasmeasured using an atomic force microscope (AFM), SPI3800N (manufacturedby Seiko Instruments Inc.). As a result, the surface roughness (Rms) ofthe plate sample was found to be 0.2 nm.

The TiO₂ concentration distribution of the foregoing plate sample wasmeasured by means of fluorescent X-ray analysis. With respect to theprocessing conditions, the condition for each site of the glasssubstrate was derived by the method described in JP-A-2007-22903. In thepresent Examples, waviness was removed by changing a beam scanning ratefor each site of the glass substrate.

Examples 1 to 6

The above-described mechanically polished plate samples were eachsubjected to finishing under conditions shown in Table 1 and then tosecond finishing (gas cluster ion beam etching) under conditions shownin Table 2. In Tables 1 and 2, the angle formed by the normal line ofthe glass substrate and an incident gas cluster ion beam onto the glasssubstrate surface is expressed as an irradiation angle.

TABLE 1 Exam- Exam- Exam- Exam- Exam- Exam- ple 1 ple 2 ple 3 ple 4 ple5 ple 6 Accelerating 30 20 20 20 20 20 voltage (kV) Cluster size 30005000 3000 3000 3000 3000 (number) Beam current 80 80 150 80 80 50 (μA)Beam diameter 8 8 8 8 8 8 (mm) Irradiation 45 45 45 80 45 2 angle (°)Source gas NF₃ NF₃ NF₃ NF₃ Ar NF₃

TABLE 2 Exam- Exam- Exam- Exam- Exam- Exam- ple 1 ple 2 ple 3 ple 4 ple5 ple 6 Accelerating 15 15 15 15 15 15 voltage (kV) Cluster size 20002000 2000 2000 2000 2000 (number) Beam current 150 150 150 150 150 150(μA) Irradiation 45 45 45 45 45 45 angle (°) Source gas O₂ O₂ O₂ O₂ O₂O₂

Examples 7 to 12

The above-described mechanically polished plate samples were eachsubjected to finishing under conditions shown in Table 3 and then tosecond finishing (touch polishing) under conditions shown in Table 4. InTable 3, the angle formed by the normal line of the glass substrate andan incident gas cluster ion beam onto the glass substrate surface isexpressed as an irradiation angle.

TABLE 3 Exam- Exam- Exam- Exam- Exam- Exam- ple 7 ple 8 ple 9 ple 10 ple11 ple 12 Accelerating 30 20 20 20 20 20 voltage (kV) Cluster size 30005000 3000 3000 3000 3000 (number) Beam current 80 80 150 80 80 50 (μA)Beam diameter 8 8 8 8 8 8 (mm) Irradiation 45 45 45 80 45 2 angle (°)Source gas NF₃ NF₃ NF₃ NF₃ Ar NF₃

TABLE 4 Exam- Exam- Exam- Exam- Exam- Exam- ple 7 ple 8 ple 9 ple 10 ple11 ple 12 Surface 10 10 10 10 10 10 pressure (gf/cm²) Average 15 to 2015 to 20 15 to 20 15 to 20 15 to 20 15 to 20 primary particle size ofcolloidal silica in polishing slurry (nm) Content of 20 20 20 20 20 20colloidal silica in polishing slurry (% by mass) pH of polishing  2  2 2  2  2  2 slurry

With respect to the samples of the foregoing Examples 1 to 12, an RMSslope (RMS1) in the region that 5 μm<λ (spatial wavelength)<1 mm, an RMSslope (RMS2) in the region that 250 nm<λ (spatial wavelength)<5 μm, anRMS slope (RMS3) in the region that 2.5 μm<λ (spatial wavelength)<1 mm,an RMS slope (RMS4) in the region that 250 nm<λ (spatial wavelength)<2.5μm, an RMS (RMS5) in the region that 100 nm<λ (spatial wavelength)<1 μmand an RMS (RMS6) in the region that 50 nm<λ (spatial wavelength)<250 nmwere measured with the above-described flatness analyzer and atomicforce microscope (AFM). The results are shown in Tables 5 and 6.

TABLE 5 Exam- Exam- Exam- Exam- Exam- Exam- ple 1 ple 2 ple 3 ple 4 ple5 ple 6 Flatness (nm) 258 612 443 356 182 325 HSFR (nm) 62 48 71 38 5558 RMS1 (mRad) 0.40 0.34 0.31 0.37 0.40 0.52 RMS2 (mRad) 0.33 0.32 0.380.42 0.41 0.51 RMS3 (mRad) 0.44 0.39 0.36 0.41 0.44 0.55 RMS4 (mRad)0.30 0.29 0.35 0.40 0.37 0.47 RMS5 (nm) 0.048 0.039 0.041 0.032 0.0450.12 RMS6 (nm) 0.09 0.11 0.11 0.10 0.12 0.11

TABLE 6 Exam- Exam- Exam- Exam- Exam- Exam- ple 7 ple 8 ple 9 ple 10 ple11 ple 12 Flatness (nm) 513 348 332 337 211 325 HSFR (nm) 44 67 51 50 7262 RMS1 (mRad) 0.38 0.34 0.29 0.39 0.39 0.59 RMS2 (mRad) 0.32 0.32 0.380.41 0.43 0.45 RMS3 (mRad) 0.42 0.38 0.35 0.43 0.41 0.62 RMS4 (mRad)0.28 0.27 0.36 0.38 0.40 0.38 RMS5 (nm) 0.038 0.044 0.032 0.038 0.0420.12 RMS6 (nm) 0.09 0.11 0.11 0.10 0.12 0.11

Under the conditions of Examples 6 and 12, RMS2, 4 and 6 were attained.However, since the driving force for the chemical material removal washigh and hence they were susceptible to the influence of materialnon-uniformity, RMS 1, 3 and 5 were not attained.

On the other hand, in Examples 1 to 3, Examples 7 to 9 and Examples 5and 11, by enhancing the driving force for the physical material removalaccording to the following changes, they were made to be not susceptibleto the influence of material non-uniformity, thereby simultaneouslyattaining RMS1 to RMS6.

In Examples 1 and 7, by increasing the accelerating voltage at the timeof finishing, the collision speed of a cluster was increased, and thedriving force for the physical material removal was enhanced, therebymaking concaves and convexes (RMS slope) of the surface small.

In Examples 2 and 8, by enhancing the size of the cluster at the time offinishing, the physical energy per unit cluster during the collision wasenhanced, thereby making concaves and convexes (RMS slope) of thesurface small.

In Examples 3 and 9, by increasing the beam current at the time offinishing, the driving force for the physical material removal wasenhanced, thereby making concaves and convexes (RMS slope) of thesurface small.

In Examples 4 and 10, by increasing the irradiation angle at the time offinishing, the cluster enters the surface of the substrate at a lowangle. As a result, the convexes of the material became readilyremovable selectively, thereby making concaves and convexes (RMS slope)of the surface small.

In Examples 5 and 11, by changing the source gas at the time offinishing from one having a large driving force for the chemicalmaterial removal to one having a small driving force, the driving forcefor the physical material removal was relatively enhanced, therebymaking concaves and convexes (RMS slope) of the surface small.

While the invention has been described in detail and with reference tospecific embodiments thereof, it will be apparent to one skilled in theart that various changes and modifications can be made therein withoutdeparting from the spirit and scope thereof.

Industrial Applicability

Since the glass substrate finished by the method of the invention isexcellent in RMS slope, RMS in an HSFR region and flatness, it issuitable for an optical element of an optical system of an exposuretool, in particular, an optical element to be used in an optical systemof an exposure tool for semiconductor production of next generationshaving a line width of 45 nm or finer; and for a photomask and a maskblank to be used for the production thereof, in particular, a reflectivetype mask for use in EUVL; and for a mask blank to be used for theproduction of the mask.

The invention claimed is:
 1. A glass substrate having a substratesurface that satisfies the following requirements (1) and (2): (1) anRMS slope in the region that 5 μm<λ (spatial wavelength)<1 mm is notmore than 0.5 mRad; and (2) an RMS slope in the region that 250 nm<λ(spatial wavelength)<5 μm is not more than 0.6 mRad.
 2. A glasssubstrate having a substrate surface that satisfies the followingrequirements (3) and (4): (3) an RMS slope in the region that 2.5 μm<λ(spatial wavelength)<1 mm is not more than 0.45 mRad; and (4) an RMSslope in the region that 250 nm<λ (spatial wavelength)<2.5 μm is notmore than 0.5 mRad.
 3. A glass substrate having a substrate surface thatsatisfies the following requirements (5) and (6): (5) an RMS in theregion that 100 nm<λ (spatial wavelength)<1 μm is not more than 0.1 nm;and (6) an RMS in the region that 50 nm<λ (spatial wavelength)<250 nm isnot more than 0.15 nm.
 4. A glass substrate having a substrate surfacethat satisfies the following requirements (3) to (6): (3) an RMS slopein the region that 2.5 μm<λ (spatial wavelength)<1 mm is not more than0.45 mRad; (4) an RMS slope in the region that 250 nm<λ (spatialwavelength)<2.5 μm is not more than 0.5 mRad; (5) an RMS in the regionthat 100 nm<λ (spatial wavelength)<1 μm is not more than 0.1 nm; and (6)an RMS in the region that 50 nm<λ (spatial wavelength)<250 nm is notmore than 0.15 nm.
 5. A photomask blank obtained from the glasssubstrate according to any one of claims 1 to
 4. 6. A photomask obtainedfrom the mask blank according to claim
 5. 7. An exposure tool using theglass substrate according to any one of claims 1 to 4 as an opticalelement of an optical system.